Question

evaluate tan 60°+ cot 30°/ sin 60°+ cot 30°​

Answer 1

Answer

tan 60 +cot 30/sin60+cot 30

√3+√3/(√3/2)+√3

√3+2+√3

2+2√3 is the answer

mark brainlist if my answer is right

Answer 2

$\large\underline{\bold{Given \:Question - }}$

$\sf \: Evaluate : \: \dfrac{tan60\degree + cot30\degree}{sin60\degree + cot30\degree}$

$\large\underline{\sf{Solution-}}$

$\sf :\longmapsto\: \: \dfrac{tan60\degree + cot30\degree}{sin60\degree + cot30\degree}$

We know that,

$\boxed{ \bf \: tan60\degree = \sqrt{3} }$

$\boxed{ \bf \: cot30\degree = \sqrt{3} }$

$\boxed{ \bf \: sin60\degree = \dfrac{ \sqrt{3} }{2} }$

• On substituting all these values, we get

$\: \: \sf \: = \: \: \dfrac{ \sqrt{3} + \sqrt{3} }{\dfrac{ \sqrt{3} }{2} + \sqrt{3} }$

$\: \: \sf \: = \: \: \dfrac{ 2\sqrt{3}}{ \: \: \: \: \dfrac{ \sqrt{3} + 2 \sqrt{3} }{2} \: \: \: \: \: }$

$\: \: \sf \: = \: \: \dfrac{4 \: \: \cancel{\sqrt{3}} }{3 \: \: \: \cancel{ \sqrt{3}} }$

$\: \: \sf \: = \: \: \dfrac{4}{3}$

$\bf\implies \: \: \dfrac{tan60\degree + cot30\degree}{sin60\degree + cot30\degree} = \dfrac{4}{3}$

Additional Information :-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$